Such an assembly is known from international patent application WO91/00041. In this known assembly, the mixing device consists of an emulsifier which, in addition to the milk inlet and the steam inlet, further comprises an air inlet. The steam inlet, air inlet and the milk inlet open into a suction chamber. Further, the known emulsifier comprises a mixing chamber which is in fluid communication with the suction chamber. The mixing chamber in turn is in communication with an outlet of the emulsifier. When steam is supplied to the steam inlet under high pressure, this will create a reduced pressure in the suction chamber. As a result, milk will be sucked in via the milk inlet and air will be sucked in via the air inlet. The thus sucked-in milk and air then move together with the steam to the mixing chamber. In the mixing chamber, frothed milk is formed which leaves the emulsifier via the outlet referred to. This frothed milk can be used for preparing cappuccino. In the known assembly, a problem occurs in that it is found that the heated milk that is dispensed is not always entirely pure. The heated milk has been found to contain traces of bad milk. As a result, the quality of the heated milk greatly deteriorates, so that the taste, the colour and the appearance of the milk dispensed are adversely affected. This may also be unhealthy. However, in the catering industry regulations may apply or may do so in the future, that impose minimum requirements regarding the quality of the milk dispensed by an emulsifying assembly.